Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

Abstract

In this article, we study reliability measures such as geometric vitality function and conditional Shannon's measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them.

Keywords:

• Generalized failure rate
• Geometric vitality function
• Shannon's measure of uncertainty

Mathematics Subject Classification:

• 62E10
• 62N05

Acknowledgment

The third author wishes to acknowledge the University Grants Commission, India for the financial assistance for carrying out this research work.

Notes

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